Question
In: Finance
Consider a project to produce solar water heaters. It requires a $10 million investment and offers...
Consider a project to produce solar water heaters. It requires a $10 million investment and offers a level after-tax cash flow of $1.56 million per year for 10 years. The opportunity cost of capital is 9.25%, which reflects the project’s business risk.
a. Suppose the project is financed with $4 million of debt and $6 million of equity. The interest rate is 5.25% and the marginal tax rate is 21%. An equal amount of the debt will be repaid in each year of the project's life. Calculate APV. (Enter your answer in dollars, not millions of dollars. Do not round intermediate calculations. Round your answer to the nearest whole number.)
b. If the firm incurs issue costs of $730,000 to raise the $6 million of required equity, what will be the APV? (Enter your answer in dollars, not millions of dollars. Do not round intermediate calculations. Round your answer to the nearest whole number. Negative amount shoud be indicated by a minus sign.)
Solutions
Expert Solution
a)
The Adjusted present value (APV) = NPV + PV of debt tax shield
| Year | Amount of debt | Interest tax shield | PV Factor | PV of interest tax shield |
| 1 | 4,000,000 | 44100 | 0.950118765 | 41900.23753 |
| 2 | 3600000 | 39690 | 0.902725667 | 35829.18174 |
| 3 | 3200000 | 35280 | 0.857696596 | 30259.53591 |
| 4 | 2800000 | 30870 | 0.81491363 | 25156.38377 |
| 5 | 2400000 | 26460 | 0.774264732 | 20487.04481 |
| 6 | 2000000 | 22050 | 0.735643451 | 16220.93809 |
| 7 | 1600000 | 17640 | 0.698948647 | 12329.45413 |
| 8 | 1200000 | 13230 | 0.664084225 | 8785.834297 |
| 9 | 800000 | 8820 | 0.630958884 | 5565.057354 |
| 10 | 400000 | 4410 | 0.599485875 | 2643.73271 |
| Total PV of tax-shield | 199177.4003 |
| Year | Cash-flows | PV Factor | PV of cash-flows |
| 0 | -10,000,000 | 1 | -10000000 |
| 1 | 1560000 | 0.915331808 | 1427917.62 |
| 2 | 1560000 | 0.837832318 | 1307018.417 |
| 3 | 1560000 | 0.766894571 | 1196355.53 |
| 4 | 1560000 | 0.701962994 | 1095062.27 |
| 5 | 1560000 | 0.642529056 | 1002345.327 |
| 6 | 1560000 | 0.588127282 | 917478.5605 |
| 7 | 1560000 | 0.538331609 | 839797.3094 |
| 8 | 1560000 | 0.492752044 | 768693.1893 |
| 9 | 1560000 | 0.45103162 | 703609.3266 |
| 10 | 1560000 | 0.412843588 | 644035.9969 |
| Net present value | -97686.4531 |
The Adjusted present value (APV) = NPV + PV of debt tax shield
APV = -97686.45 + 199177.40
APV = $101491
(b)
The costs of $730,000 to raise the $6 million of required equity are the floatation costs
APV (with floatation costs) = NPV + PV of debt tax shield - flotation cost
Hence, APV = -97686.45 + 199177.40 - 730000 = - 628509.05
APV = -$628509
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